Embeddings of nonorientable surfaces with totally reducible focal set
| Autor: | Ridvan Ezentas, Sheila Carter |
|---|---|
| Přispěvatelé: | Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü., Ezentaş, Rıdvan |
| Rok vydání: | 1994 |
| Předmět: | |
| Zdroj: | Glasgow Mathematical Journal. 36:11-16 |
| ISSN: | 1469-509X 0017-0895 |
| DOI: | 10.1017/s0017089500030494 |
| Popis: | In an earlier paper [5] we introduced the idea of an immersion f:M W with totally reducible focal set.Such an immersion has the property that, for all peM, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at .Trivially, this always holds if n=m+1 so we only consider n > m + 1.In [5] we showed that if M2 is a compact surface then for all n>4 there is a substantial immersion:A/2 R with totally reducible focal set. Further, if M2 is orientable or is a Klein bottle or a Klein bottle with handles then/:M2 W can be taken to be an embedding.Here we show that if M2 is a projective plane or a projective plane with handles then for all 5 there exists a substantial embedding f:M2 M with totally reducible focal set although,by arguments of M. Gromov and E. G. Rees,for n=4 such an embedding does not exist. |
| Databáze: | OpenAIRE |
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